Effect of Rainfall and Water Level Rise and Fall on Stability of Core Wall Embankment

Abstract

Transient seepage triggered by rainfall and water level changes has a significant impact on embankment stability. To investigate the effects of rainfall and water level changes on the seepage field of embankments, numerical comparative experiments were conducted based on the Shu River embankment project. The influence of key factors such as rainfall, water level rise and fall rate, and rainfall-coupled water level rise and fall on the internal seepage field of the embankment was analyzed, and the main factors affecting the stability of the embankment slope were identified. The relationship among permeability coefficient, lag rate of the phreatic line, and embankment slope stability factor is explored, and fitting equations are developed. The results show that rainfall infiltration increases the pore water pressure of the soil, leading to a decrease in the effective stress of the soil and a decrease in the slope stability factor. The stability factor of the embankment slope is positively correlated with the rise and fall of the water level, and the faster the rate of rise and fall, the higher the rate of change in pore water pressure. The stability factor of the embankment slope showed a trend of decreasing and then increasing with the decrease in water level, and when the water level had decreased by 70%, the lag rate of the phreatic line was the largest, and the stability factor of the embankment slope was the lowest. The established equations for fitting the stability factor of the embankment slope to the lag rate of the phreatic line can be used as a reference for the safety assessment of similar embankment projects.

1. Introduction

China is one of the countries most severely affected by floods in the world, with half of the country’s population and most of its wealth concentrated near rivers and flood-prone flood protection zones [1,2,3]. Up to now, China has built a total of 330,600 km of embankments of all types at level 5 and above, protecting 682 million people and 629 million mu of arable land. An embankment failure would result in serious human and economic losses [4,5,6]. Relevant studies have shown that rainfall and changes in water levels are the main causes of failure of sand embankments [7,8,9]. Rainfall and water level rise and fall affect the pore water pressure, soil strength, and sliding surface stability of slopes by altering the water distribution and stress state of the soil [10,11,12], thus leading to slope instability [13,14,15]. For this reason, it is particularly necessary to carry out research on the effects of rainfall and water level rise and fall on the stability of core wall embankments.

Numerous scholars have conducted a lot of research on the stability of embankments and have achieved certain results pertaining to aspects of rainfall action on embankment stability. TANG et al. [16] studied and analyzed the stability of unsaturated slopes under the Random Rainfall Pattern (RRP) model from three perspectives and found that slope stability depends on the temporal distribution of rainfall intensity. Chang et al. [17] analyzed the effect of rainfall on factors such as volumetric water content, pore water pressure, and horizontal earth pressure of loess slopes through indoor experiments to illustrate the slope damage mechanism. Jiang et al. [18] and Zeng et al. [19] investigated the change rule of transient saturated zone on slopes under rainfall by finite element simulation and concluded that the formation and expansion of transient saturated zone are closely related to the intensity and duration of rainfall. et al. [20] and Cen et al. [21] used finite element software to simulate and analyze the change pattern of embankment stability under the effect of rapid decrease in upstream water level. GAO et al. [22] used FLAC simulation to analyze the effect of slope gradient, slope permeability coefficient, and rate of water level drop on slope stability and found that the slope stability factor is minimum when the water level drops by two-third. Sun et al. [23,24,25] explored in detail the effects of water level fluctuation rate and soil permeability coefficient on slope stability based on a combined finite element–discrete element method, as well as the effect of combined rainfall-coupled water level changes on embankment stability. Jiang et al. [26] found that the deformation rate of the leading edge of the slope is directly proportional to the rate of water level drop through large-scale physical modeling tests, and traction damage occurs in the easy slope under the combined effect of rainfall and water level drop. JIAN et al. [27] used FLAC3D simulation to analyze the slope landslide process and found that the rising water level and continuous rainfall led to a great increase in the shear strain, displacement, and shear damage area of slopes, which induced the slope landslide collapse. Sun et al. [28] proposed the calculation method of infiltration line and the analysis method of slope stability factor under fluctuating water levels by studying and analyzing the evolution process of slope landslides under the joint action of fluctuating water levels and rainfall. Yang et al. [29] by analyzing the change rule of slope stability factor under water level fluctuation and rainfall found that the change trend of slope stability factor is basically consistent with the change in reservoir water level, and the minimum value of the safety coefficient appeared in the period of water level decline. Although scholars at home and abroad have performed a lot of research on the stability of embankment under the effect of rainfall coupled with water level change, the stability of embankment is affected by more factors, which need to be further considered and analyzed.

Based on this, this paper takes the sandy embankment of Shushi River as the research object and conducts numerical comparative tests using Geo-Studio. The effects of key factors such as river water level height, water level rise and fall rate, and rainfall–water level coupling on the pore water pressure within the embankment were investigated, and the main factors affecting the stability of the embankment were clarified. The relationship between permeability coefficient, lag rate of the phreatic line, and embankment slope stability factor was further explored, and a fitting equation between lag rate of the phreatic line and embankment slope stability factor was established. The results of the study provide a reference for seepage safety assessment of core wall embankments.

2. Engineering Overview and Numerical Model

2.1. Engineering Background

Shu River is one of the backbone rivers in the Yishuv-Si River Basin, flowing southwards through Shandong Province and Jiangsu Province, with a total length of 300 km and a watershed area of 6400 km². According to statistics, from 1280 to 1948, there were 364 floods. From 1949 to 1984, the average annual flood-affected area was 7.74 million mu, accounting for 14.2% of the cultivated land area in the river basin across two provinces. The Shu River is a rain-fed flash flood channel, with flooding primarily occurring during the main flood season, and is characterized by high flow rates and rapid flow speeds. Based on the characteristics of heavy rainfall and flooding in the Shu River Basin and the analyses of the catchment pattern, flooding in the Shu River Basin is mainly caused by short-term heavy rainfall. The geotechnical composition of the river embankment mainly consists of sandy soil, which is prone to seepage failure under hydraulic scour, as shown in Figure 1. At present, the embankment cross-sections are inadequate, with numerous hazardous river sections and insufficient flood control standards. Frequent flooding poses a serious threat to the safety of residents along the riverbanks. Therefore, urgent remediation is required to establish a comprehensive flood protection system.

2.2. Calculation Model

To study the impact of rainfall and water level fluctuations on the stability of the core wall embankment, a representative cross-section was selected, as shown in Figure 2.

(1)

Model dimensions: The height and top width of the embankment is 6 m. The upstream and downstream slope ratio is 1:1.25. The embankment is filled with gravelly medium-coarse sand. The core wall is made of clay with a top width of 1 m and a bottom width of 2.5 m. The embedment depth of the core wall is 1 m. The design flood level is 4 m.

(2)

Monitoring points: Monitoring points P_i, H_i, and L_i are located at the upstream, downstream, and center sections of the core wall embankment. The heights of P₁, P₂, and P₃ are 10.5 m, 9.0 m, and 7.5 m, respectively. The heights of L₁, L₂, and L₃ are 10.5 m, 9.0 m, and 7.5 m, respectively. The heights of H₁, H₂, and H₃ are 6.3 m, 5.8 m, and 5.3 m, respectively. All monitoring points P_i, H_i, and L_i are positioned 0.5 m from the embankment surface

(3)

Boundary condition: Geo-studio software (2022) was used to conduct seepage–stress–stability coupled analysis. The model adopts quadrilateral mesh division. The upstream embankment slope bd is the water level fluctuation boundary, efg is the drainage boundary, ghab is the impermeable boundary, and during rainfall, defg is the flow boundary.

2.3. Calculation Parameters and Working Condition Design

2.3.1. Calculation Parameters

(1)

Rainfall: It is distributed throughout the year, with 50% occurring in July and August. The most intense rainstorms typically occur in July, as shown in Figure 3. On average, over many years, 85.5% of the maximum 72 h rainfall occurs within the first 24 h, while 64.1% of the maximum 72 h flood volume occurs within the first 24 h. In this study, the July rainfall is considered the most unfavorable seepage boundary condition, with a rainfall intensity of 30 mm/day and a duration of 72 h.

(2)

Rate of Water Level Rise and Fall: The initial river water level is 5 m, and the design flood level is 9 m, resulting in a water level fluctuation of 4 m. To study the impact of the rate of water level change on the pore water pressure within the embankment, it is assumed that the rates of rise and fall are 0.8 m/day (denoted as v₁), 2 m/day (denoted as v₂), and 4 m/day (denoted as v₃), respectively.

(3)

Material Parameters: The material parameters for different regions of the core wall embankment are determined based on field investigations and laboratory tests. It is assumed that the materials in each region are isotropic, with their physical and mechanical parameters listed in

Table 1. Physical and mechanical parameters of materials in different regions of the core wall embankment.

Material Name	Permeability Coefficient (m/s)	Saturated Volumetric Water Content	Angle of Internal Friction (°)	Cohesion (kPa)	Young’s Modulus (MPa)	Poisson’s Ratio	Density (g/cm−3)
Embankment Foundation	1.07 × 10−4	0.27	30	10	80	0.33	2.0
Embankment Body	5.88 × 10−5	0.29	27	8	70	0.30	1.8
Core Wall	1.12 × 10−8	0.01	8	32	60	0.20	1.9

. The Fredlund–Xing model is used in this study to obtain the volumetric water content function for unsaturated soil, as shown in Figure 4.

2.3.2. Working Condition Design

In order to clarify the effects of water level changes and rainfall on the pore water pressure inside the embankment, three types of working conditions were formulated, i.e., Type A conditions (different water level heights coupled with rainfall), Type B conditions (different water level rise and fall velocities), and Type C conditions (different rise and fall velocities coupled with rainfall), as shown in

Table 2. Working conditions table.

Working Conditions	Research Content	Sub-Working Conditions	River Water Level (m)	Rate of Change in Water Level (d/mm)	Rainfall
A	different river water levels	A1	5	—	the most adverse rainfall
		A2	9	—
B	different water level rise and fall rates	B1	5~9	v1 = 0.8	—
		B2		v2 = 2.0	—
		B3		v3 = 4.0	—
C	coupled rainfall with different rates of change in water levels	C1	5~9	v1 = 0.8	the most adverse rainfall
		C2		v2 = 2.0
		C3		v3 = 4.0

.

3. A Study of the Key Factors Influencing Embankment Stability

Changes in pore water pressure have a direct impact on embankment stability, particularly under conditions such as rainfall and fluctuations in water levels. Variations in pore water pressure can lead to changes in effective stress and permeability within the embankment [30]. Therefore, this study analyzes the pore water pressure within the embankment under different water level heights coupled with rainfall.

3.1. Analysis of Pore Water Pressure Under Different Water Level Heights Coupled with Rainfall

The working conditions (A₁~A₂) are compared and analyzed with river water levels as the variable. To clarify the patterns of pore water pressure changes within the embankment under the effects of coupled rainfall at different water level heights, comparative analyses of pore water pressure at various monitoring locations were conducted.

3.1.1. Pore Water Pressure Analysis Under Low Water Level Coupled with Rainfall (Case A₁)

As shown in Figure 5, the area of unsaturated zone soil within the embankment decreases with the duration of rainfall. The variation in pore water pressure at each measurement point under low water level coupled with rainfall is shown in Figure 6.

As shown in Figure 6, the pore water pressure inside the embankment increases with the duration of rainfall. Once the upper soil layer reaches a temporarily saturated state, water infiltrates deeper into the embankment due to gravitational potential energy. Consequently, the farther the distance from the embankment surface, the greater the delay in pore water pressure change. Specifically, P₁ < P₂ < P₃, L₁ < L₂ < L₃, and H₁ < H₂ < H₃. As shown in Figure 6a, the initial pore water pressures at measurement points P₁, P₂, and P₃ are −43 kPa, −32.228 kPa, and −17.517 kPa, respectively, and the pore water pressure at measurement point P₁ reaches a peak value of 4.322 kPa at 18 h, with an amplitude of 47.322 kPa, and then decreases gently to a stable state of 2.764 kPa. The pore water pressure at measurement points P₂ and P₃ peaked at 4.692 kPa and 3.756 kPa at 29 h and 36 h, respectively, with variation amplitudes of 36.920 and 21.373, respectively, and then stabilized at 2.870 kPa. The response rate of the pore water pressure at the measurement point P_i was P₁ > P₂ > P₃. As shown in Figure 6b, the pore water pressure changes at measurement points L₂ and L₃ exhibit significant delays, with increases starting at 12 h and 36 h, respectively. This phenomenon occurs because measurement points L₂ and L₃ are located next to the core wall. The core wall has a low permeability coefficient, which interferes with the transport paths and fronts of the wetting front, reducing the infiltration rate and causing the pore water pressure changes at L₂ and L₃ to lag significantly. According to Figure 6c, the pore water pressure trends at measurement points H₁ and H₂ are similar to those at measurement points P_i and L_i, while the magnitude of pore water pressure change at H₃ is relatively smaller.

3.1.2. Pore Water Pressure Analysis Under High Water Level Coupled with Rainfall (Working Condition A₂)

As shown in Figure 7, the area of the unsaturated soil body gradually decreases and moves downward under the effect of rainfall. After 72 h of rainfall, the soil reaches a critical saturation state. The variation in pore water pressure at each measurement point under high water level coupled with rainfall is shown in Figure 8.

As shown in Figure 8a, the initial pore water pressure at measurement point P₁ is −9.116 kPa, and it increases with the duration of rainfall, reaching a peak value of 2.935 kPa at 14 h. Measurement point P₂ is located at the designed flood level, while P₃ is below the flood level. Both P₂ and P₃ remain saturated, with pore water pressures stabilized at 5.159 kPa and 14.212 kPa, respectively. Figure 8b shows that the pore water pressure at measurement point L₁ follows a trend of first increasing, then decreasing, and finally stabilizing. The pore water pressures at measurement points L₂ and L₃ began to increase at 7 h and 14 h, respectively. Compared to the low water level coupled with rainfall, the lag time of pore water pressure changes at L₂ and L₃ is shortened. The time to reach peak pore water pressure at measurement points L₁, L₂, and L₃ occurred in the order L₃ > L₂ > L₁. According to Figure 8c, the pore water pressure at measurement points H₃ and H₂ increases slowly over time with rainfall, showing a relatively small range of variation. In contrast, the pore water pressure at measurement point H₁ significantly increases with the duration of rainfall, reaching a peak of 1.869 kPa after 22 h. In summary, rainfall primarily affects the unsaturated soil above the phreatic line, with a lesser impact on the soil below it. The saturated soil beneath the phreatic line is mainly influenced by the water level height. There is a “response delay” phenomenon in the changes in pore water pressure, with the delay time positively correlated to the distance of the soil from the top of the embankment. In other words, the pore water pressure response rate is higher in shallow soil compared to deeper soil.

3.2. Analysis of the Effect of Water Level Rise and Fall Velocity on Pore Water Pressure

As shown in Figure 9, during the process of water level fall, the rate of water level fall is positively correlated with the height of the phreatic line. When the water level falls rapidly, the water inside the embankment is not discharged in time, causing the phreatic line to be higher than the upstream water level, generating an outward seepage force that is unfavorable for embankment stability. During the process of water level rise, the rate of water level rise is negatively correlated with the height of the phreatic line. When the water level rises rapidly, water does not fully penetrate the embankment, causing the phreatic line to be lower than the upstream water level, generating an inward seepage force, which provides a certain slope protection effect.

This type of condition (B₁~B₃) uses the rate of river water level rise and fall as the variable. As shown in Figure 10, when the river water level is at 9 m, measurement points P₃ and H₃ are located below the phreatic line. To clarify the effect of the water level rise and fall rate on the pore water pressure within the embankment, a comparative analysis of the pore water pressure at points P₃ and H₃ was performed. The effect of the water level rise and fall rate on the pore water pressure at measurement points P₃ and H₃ is illustrated in Figure 11.

As shown in Figure 11, the pore water pressure changes at measurement points P₃ and H₃ are positively correlated with the water level rise and fall. When the river water level is at 9 m, the initial pore water pressure at measurement point P₃ is 14.212 kPa. As the water level drops to 5 m at rates of 0.8 m/d, 2 m/d, and 4 m/d, the corresponding pore water pressures decrease to −9.526 kPa, −7.131 kPa, and −5.512 kPa, respectively, representing reductions of 23.738 kPa, 21.346 kPa, and 19.734 kPa. The slower the water level drops, the greater the magnitude of pore water pressure change, as shown in Figure 11a. Although the change pattern of pore water pressure at measurement point H₃ is similar to that at P₃, the magnitude of change at H₃ is smaller than that at P₃. In conclusion, the slower the rate of water level decline, the more time is allowed for drainage within the embankment soil, resulting in lower pore water pressure values and greater changes in magnitude. When the water level drops rapidly, the internal water in the embankment is not discharged in time, causing the internal pore water pressure to remain at a higher level. This leads to a significant internal–external pressure difference, which is unfavorable for embankment stability. Due to the excellent impermeability of the core wall, water level changes primarily affect the upstream side of the embankment.

3.3. Analysis of the Impact of Coupled Effects of Water Level Rise and Fall and Rainfall on Pore Water Pressure

The working conditions (C₁~C₃) use the rate of water level rise and fall as the variable. As shown in Figure 12a, a faster water level rise corresponds to a lower phreatic line height and a larger area of unsaturated zone soil. In Figure 12b, it is observed that, under the combined effect of water level rise and rainfall, the area of unsaturated zone soil decreases.

To clarify the pattern of pore water pressure changes within the embankment under the combined effects of water level fluctuations and rainfall, a comparative analysis of the pore water pressure at monitoring points P_i and H_i was conducted. The changes in pore water pressure at monitoring points P_i and H_i under the combined effects of water level rise and fall and rainfall are shown in Figure 13.

From Figure 13a,c, it can be observed that the pore water pressures at measurement points P_1,2 and H_1,2 initially increase, then decrease, and eventually stabilize under the combined effects of water level rise and rainfall. The rate of water level rise and fall does not affect the pore water pressure at these measurement points. The pore water pressure at measurement points P₃ and H₃ increases over time. The faster the rate of water level rise, the higher the rate of change in pore water pressure, resulting in a steeper curve. Figure 13b shows that pore water pressure at measurement point P₃ exhibits a trend of an initial rapid decrease followed by a gradual decline over time. The faster the rate of water level decline, the higher the rate of decrease in pore water pressure. At measurement point P₂, the pore water pressure first decreases, then increases slowly, and eventually stabilizes under the combined effects of water level decline and rainfall. Measurement point P₁, located at the top of the embankment’s upstream side and primarily influenced by rainfall, shows a continuous increase in pore water pressure over time, eventually stabilizing once saturation is reached. As shown in Figure 13d, the pore water pressure at measurement points H₂ and H₃ is mainly influenced by water level changes, decreasing as the water level drops. The slower the water level declines, the greater the reduction in pore water pressure. Measurement point H₁ is primarily affected by rainfall. Under the combined influence of water level decline and rainfall, the pore water pressure at H₁ shows a trend of initially increasing before stabilizing. Changes in the rate of water level decline do not affect the pore water pressure at H₁.

4. Analysis of the Effect of Water Level Rise and Fall Coupled with Rainfall on Embankment Stability

4.1. Stability Analysis of Embankments

Water level changes and rainfall are significant factors affecting the seepage stability of embankments. Water level changes typically involve two scenarios: water level rise and water level fall. Both scenarios influence the distribution of seepage pressure and flow within the embankment, thereby impacting its seepage stability. Rainfall affects seepage stability primarily by increasing the embankment’s water content, particularly during heavy or prolonged rainfall. Therefore, it is crucial to consider the combined effects of water level changes and rainfall on embankment seepage stability.

4.1.1. Effects of Water Level Rise Coupled with Rainfall on the Stability of Embankment Slopes

Both water level rise and rainfall infiltration change the soil’s water content, leading to variations in pore water pressure and affecting slope stability. Figure 14 shows the changes in the slope stability factor of the upstream embankment under water level rise and the combined effect of water level rise and rainfall.

Figure 14a shows that the stability factor of the embankment slope increases with rising water levels. The faster the water level rises, the higher the stability factor, indicating that higher water levels can provide a certain degree of slope protection. Under the combined effect of rising water levels and rainfall, the initial stability factor of the embankment slope decreases; however, as the water level continues to rise, the stability factor gradually increases. Thus, the impact of rising water levels on the stability factor of the embankment slope is greater than the impact of rainfall. From Figure 14b, the stability factor of the embankment slope F_s is 1.465 when the initial river water level is 5 m. As the river water level rises to 9 m at rates of 0.8 m/d, 2 m/d, and 4 m/d, the stability factor F_s increases to 2.012, 2.076, and 2.156, representing increases of 32%, 42%, and 47%, respectively. The faster the water level rise, the greater the increase in the stability factor. Under the combined influence of rainfall and rising water level, the initial stability factor F_s decreases from 1.465 to 1.336. When the water level rises to 9 m at rates of 0.8 m/d, 2 m/d, and 4 m/d, the stability factor increases to 1.797, 1.874, and 1.961, representing gains of 35%, 40%, and 46%, respectively. Rising water levels enhance slope stability, while rainfall reduces slope stability and decreases the magnitude of changes in the stability factor.

Cause analysis: Rainwater infiltration increases the pore water pressure inside the embankment, reducing the effective stress in the soil, which in turn decreases the soil’s shear strength and increases the possibility of slope failure. Compared to rainfall infiltration, water level changes have a more significant impact on slope stability. When the water level rises, the difference in hydraulic head causes inward seepage, generating an inward seepage force that opposes the potential sliding direction, temporarily stabilizing the slope by inhibiting the development of the plastic zone. Additionally, the external pressure exerted by the water on the upstream slope increases with the rising water level, and this hydraulic action can further suppress slope sliding in the short term.

4.1.2. Effects of Water Level Fall Coupled with Rainfall on the Stability of Embankment Slopes

Changes in the stability factor of the embankment slope upstream under the effect of water level fall and under the combined effect of water level fall and rainfall are shown in Figure 15.

Figure 15a shows that the stability factor of the embankment slope shows a tendency of decreasing and then increasing with the decrease in the water level. The faster the water level falls, the lower the stability factor of the embankment slope. When the water level decrease percentage reaches 0.7, it is the most dangerous water level, and the stability factor of embankment slope is the lowest. After the water level drop rate exceeds 0.7, the stability factor of the embankment slope begins to rise. Under the combined effect of water level decline and rainfall, the stability factor of the embankment slope is further reduced, increasing the risk of seepage failure. From Figure 15b, F_s is 1.573 at the initial height of the river water level of 9 m. F_s decreases by 12%, 14%, and 17% when the water level decreases from 9 m to 5 m at the rate of 0.8 m/d, 2 m/d, and 4 m/d, respectively. Under the effect of decreasing water level coupled with rainfall, F_s decreased from 1.573 to 1.551. F_s decreased by 13%, 15%, and 18% when the river water level decreased from 9 m to 5 m at the rate of 0.8 m/d, 2 m/d, and 4 m/d, respectively. Rainfall exacerbated the risk of dike slope instability.

In summary, after the water level decreases, the pore water pressure inside the embankment remains high and does not dissipate in time, leading to an inward seepage force that adversely affects embankment stability, resulting in a lower slope stability factor. When the rate of water level decrease exceeds 0.7, the pore water pressure inside the embankment gradually decreases, the seepage force diminishes, and the effective stress of the soil increases, which enhances shear strength and allows slope stability to begin recovering, causing the slope stability factor to rise.

4.2. Discussion on the Relationship Between Slope Stability Factor and Permeability Coefficient

The permeability of the soil determines the rate of pore water pressure dissipation, affecting the stability of the embankment slope. During the water level decline, a “response delay” in the change in pore water pressure within the embankment creates an imbalance between internal and external water pressures, significantly reducing slope stability.

4.2.1. The Effect of the Permeability Coefficient of the Embankment Body on the Stability Factor of the Embankment Slope

Assuming the river water level decreases from the design flood level of 9 m to 5 m, with descent rates of 0.8 m/d, 2.0 m/d, and 4.0 m/d (denoted as v₁, v₂, and v₃, respectively), the required times are 120 h, 48 h, and 24 h. The permeability coefficients of the embankment body are set at 5.0 × 10⁻⁴ m/s, 1.0 × 10⁻⁴ m/s, 5.0 × 10⁻⁵ m/s, and 1.0 × 10⁻⁵ m/s (denoted as k₁, k₂, k₃, and k₄, respectively). The variation curves of the stability factor of the embankment slope and the permeability coefficient during the water level decline are shown in Figure 16.

From Figure 16, when the water level is at 9 m and the permeability coefficients of the embankment body are 5.0 × 10⁻⁴ m/s, 1.0 × 10⁻⁴ m/s, 5.0 × 10⁻⁵ m/s, and 1.0 × 10⁻⁵ m/s, the initial slope stability factors Fs are 1.517, 1.540, 1.564, and 1.590, respectively. A lower permeability coefficient of the embankment body results in a higher initial slope stability factor Fs. When the water level decrease percentage is between 0 and 0.3, the permeability coefficient of the embankment body is negatively correlated with the slope stability factor. Between 0.3 and 1.0, the correlation becomes positive. At around 0.7 water level decrease percentage, the slope stability factor is at its lowest, indicating the most dangerous water level. The slope stability factor initially decreases and then increases as the water level drops. Once the water level decrease percentage exceeds 0.7, the slope stability factor begins to recover.

In summary, the pore water pressure within the embankment exhibits a lag effect. As the upstream water level decreases, the low permeability of the embankment soil results in insufficient drainage, causing the pore water pressure to remain high and generating outward seepage forces, which reduce slope stability. As the water level continues to fall, the pore water pressure within the embankment gradually decreases, the effective stress of the soil increases, and the slope stability factor gradually recovers and rises.

4.2.2. Discussion on the Relationship Between Slope Stability Factor and Lag Rate of the Phreatic Line

The stability of the embankment slope primarily depends on the distribution of pore water pressure within the embankment. The slope stability factor decreases first and then increases as the water level drops, with the lowest point corresponding to the most critical water level, where the stability factor is at its minimum. By extracting the slope stability factor at the most critical water level from Figure 16, a graph of the relationship between the lag rate of the phreatic line and the permeability coefficient, as well as a graph showing the relationship between the minimum slope stability factor (F_s,min) and the lag rate of the phreatic line, is plotted, as shown in Figure 17.

From Figure 17, when k_i is fixed, a faster water level drop rate v leads to a higher lag rate of the phreatic line and a lower embankment slope stability factor F_s. When v_i is fixed, a smaller permeability coefficient k results in a higher lag rate of the phreatic line and a lower F_s. Fitting the scatterplot of the stability factor and the lag rate of the phreatic line in Figure 17b gives the following:

$$F_s=-0.187x+1.369,R^2=0.96$$

(1)

$$x=1-\Delta h_{\mathrm{p}}/\Delta h_{\mathrm{w}}$$

(2)

In this equation, x represents the lag rate of the phreatic line, $\Delta h_{\mathrm{p}}$ is the phreatic line drop height, and $\Delta h_{\mathrm{w}}$ is the water level drop height. Equation (1) demonstrates a strong linear relationship between the embankment slope stability factor and the lag rate of the phreatic line. According to Equation (1), when the internal lag rate of the phreatic line exceeds 0.64, the slope stability factor will fall below the allowable value of 1.25. For similar core wall embankment projects, interpolation from Figure 17a can be used to determine the maximum internal lag rate of the phreatic line during the water level drop. By substituting the lag rate into Equation (1), the minimum stability factor during the water level drop can be calculated, providing a reference for the safety evaluation of core wall embankments in operation.

5. Conclusions

This paper conducts a comparative study using Geo-studio under multiple working conditions. It analyzes the variation patterns of pore water pressure under different river water levels, different rates of water level rise and fall, and different rates of water level rise and fall coupled with rainfall. The relationships among permeability coefficient, lag rate of the phreatic line, and stability coefficient of the embankment slope are discussed. The main conclusions are as follows:

(1)

There is a lag phenomenon in the change in pore water pressure inside the embankment, and the lag time of the change in pore water pressure is positively correlated with the depth of the soil body. Rainfall infiltration leads to a rise in pore water pressure and a decrease in the effective stress of the soil body, which in turn reduces the stability of the embankment slope.

(2)

When the water level changes, the faster the rate of water level rise and fall, the steeper the pore water pressure change curve and the higher the rate of change. When the water level rises, the seepage force from the outside to the inside has a slope protection effect and improves the stability of the embankment slope. When the water level falls, the seepage force from the inside to the outside is in the same direction as the landslide, leading to a decrease in the stability of the embankment slope.

(3)

The stability factor of the embankment slope is related to the permeability coefficient. When the water level decrease percentage is between 0.0 and 0.3, the permeability coefficient of the slope is negatively correlated with the slope stability factor. When the water level decrease percentage is between 0.3 and 1.0, the permeability coefficient is positively correlated with the slope stability factor. The slope stability factor decreases initially and then increases as the water level decreases. At a water level decrease percentage of 0.7, the embankment slope reaches its most critical point, with the lowest stability factor.

(4)

A fitting formula between the slope stability factor and the lag rate of the phreatic line is established. This formula can quickly assess the minimum stability factor of the embankment slope during the water level drawdown process, providing a theoretical reference for the operational safety of core wall embankments.